Acceptable compact Lie groups

In this paper we show that for a connected compact Lie group to be acceptable it is necessary and sufficient that its derived subgroup is isomorphic to a direct product of the groups $\text{SU}(n)$, $\text{Sp}(n)$, $\text{SO}(2n+1)$, ${\text{G}}_2$, $\text{SO}(4)$. We show that there are invariant functions on ${\text{SO}}_4(\mathbb{C}{)}^2$ which are not generated by 1-argument invariants, though the group ${\text{SO}}_4(\mathbb{C})$ is acceptable.